% !TEX root = ArticoloRF.tex
%Random Project Details
\subsection{Extremely Randomized Trees}
In this version of the Random Forest classifier no assumption is made as far as the feature is concerned.
Let $\mathbf{X}$ denote the set of records as described in section \ref{sec:relwork}.
The split function is defined as
 \[f(\mathbf{x})=f(\mathbf{x},\mathbf{w})=\mathbf{w}\tran \mathbf{x}\]
where $\mathbf{w}$ is defined as
\[ \mathbf{w}\tran = \begin{bmatrix}w_{1}&w_{2}&\cdots&w_{n}\end{bmatrix} \]
and each $w_{i}$ is subject to the following conditions
\[ w_{i} \in \{0,1\} \]
\[ \sum_{j=0}^{n} w_{j} = 1\] 

At the time of the split, both $\mathbf{w}$ and $t$ are randomly chosen.
The threshold value is selected at random from the set $\lbrace f(\mathbf{x}): \mathbf{x}\in \mathbf{X}\rbrace$.
This procedure is iterated until the construction of the trees is over.
